Maximum ratio of (graph) irregularities
Fuente:
arXiv
Salvato in:
| Autori principali: | , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2026
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866915962770423808 |
|---|---|
| author | Cambie, Stijn Chang, Jionghua |
| author_facet | Cambie, Stijn Chang, Jionghua |
| contents | We estimate the maximum ratio between the $σ_t$- and $σ$-irregularity for graphs and trees of order $n$, which are respectively bounded by $Θ(n^{5/2})$ and $n-2$. This answers a question and a conjecture by Filipovski et al. in an elegant way. For trees, we obtain that the (Albertson) irregularity measure $\irr$ is an upper bound for the graph variance (normalised with the order). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_25341 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Maximum ratio of (graph) irregularities Cambie, Stijn Chang, Jionghua Combinatorics 05C35, 05C05, 05C09 We estimate the maximum ratio between the $σ_t$- and $σ$-irregularity for graphs and trees of order $n$, which are respectively bounded by $Θ(n^{5/2})$ and $n-2$. This answers a question and a conjecture by Filipovski et al. in an elegant way. For trees, we obtain that the (Albertson) irregularity measure $\irr$ is an upper bound for the graph variance (normalised with the order). |
| title | Maximum ratio of (graph) irregularities |
| topic | Combinatorics 05C35, 05C05, 05C09 |
| url | https://arxiv.org/abs/2604.25341 |